Potato, everything, by definition, can be said to be manipulation. Manipulation is attempting to elicit a certain response/action from someone. It's NOT a dirty word.
When I stop a stranger on the street and say, "Excuse me, but would you please direct me to Main Street?" That's manipulation, as I'm trying to get someone to give me directions and I'm using social graces, such as "excuse me and please and thank you" to get them to respond. Same with asking someone to "please pass the butter" or "do you have the time?".
It IS manipulation, and it's not natural, it's an act, because we could go up to these very same strangers and simply demand our needs, just like when we were infants and cried out that we were hungry when we wanted to be fed. "Hey YOU!", we could say, "Tell me how to get to Main Street!" but that wouldn't likely achieve the intended aim, right? We learn that. We learn how we must act and what we must do in order to hopefully get the desired outcome.
We don't go up to our boss and say, "I really hate working for you. You're quite a jerk. Now, give me more money in my paycheck." No! We learn how to negotiate, and successful negotiation is part manipulation. We have to make the party across the table believe that they are winning for them to give us what we want.
In interpersonal relationships, we have desired outcomes as well.
In this case, BipedGod's gal is using some sort of such dynamics to elicit him to draw closer to her. That's not the problem, as I see it. She wants him.
The problem is, that he believes that by him not letting her know she's using tactics that he'll be perceived as being a "dumb sh*t who hasn't a clue".
The issue then, is really more about him and his *projecting* this negative self-image upon her, as if she would think it, this belief he has about how she'd negatively perceive him, and why he'd think that way, then it is about her and whatever she's actually thinking (which, since she's trying to get him to chase her, may be more like she thinks very highly of him, rather than thinking he's stupid).
Whether she's acting consciously or not, she's responding to his being distant. The best way to respond when a partner distances, is to stay distant yourself. Otherwise, this push/pull dance never ends. She'll more likely either give up or draw close to you, if you keep distant.
No "confrontation" needed. That's useless. She may not even be aware of what she's doing, as it's normal for her. Or she could deny it. Or argue with you over it. Or claim it's because you are distant or... Actions, not words, work better. Exactly what you were doing, BipedGod, i.e., the not responding to it, not acknowledging it, not letting it interfere with your life, is exactly the right thing to do. As I wrote above, remaining independent and keeping space is the way to go.
Sometimes, NOT doing anything is the desirable option. Not everything needs an action taken.
The only thing you should do is change your opinion about how it makes you appear to her: You're only a "dumb sh*t" - if you believe you are.